As far as I remember, without rewatching the episode, they never gave a date. The script doesn't seem to have one either, although I only skimmed it and may have missed it. If you want to check it, it's at
GGGOH Script. One caveat is that the online scripts don't always follow the filmed version exactly; some are earlier versions than others.
This fandom is very forgiving, and I doubt you'd get flamed for changing a date if one existed. You could explain your rationale in a note if you're concerned about someone's reaction. You could also up front say that the story doesn't follow canon exactly. Which as far as I'm concerned all fanfic is, otherwise it's plagiarism. Besides, the "what if..." is part of the the fun of fanfic!
Glad to see you're working around your writer's block and hope to read your story soon.
